Sparse sampling using a programmatically randomized signal modulating a carrier signal

ABSTRACT

A method and a system are for sparse sampling utilizing a programmatically randomized signal for modulating a carrier signal. The system includes a compound sparse sampling pattern generator that generates at least one primary carrier signal, and at least one secondary signal. The at least one secondary signal modulates the at least one primary signal in a randomized fashion.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH AND DEVELOPMENT

This invention was made in part by Government support under ContractNumbers SB1341-15-CN-0050 and SB 1341-16-SE-0203 awarded by the NationalInstitute of Standards and Technology. The Government may have certainrights in this invention.

SUMMARY

In one embodiment, a system is provided. The system includes a compoundsparse sampling pattern generator that generates at least one primarycarrier signal, and at least one secondary signal. The at least onesecondary signal modulates the at least one primary signal in arandomized fashion.

In another embodiment, a method is provided. The method includesgenerating, by a compound sparse sampling pattern generator, at leastone primary carrier signal. The method also includes generating, by thecompound sparse sampling pattern generator, at least one secondarysignal that modulates the at least one primary signal in a randomizedfashion.

In yet another embodiment, a scanning probe instrument is provided. Thescanning probe instrument includes a compound sparse sampling patterngenerator that generates at least one primary carrier signal, and atleast one secondary signal that modulates the at least one primarysignal in a randomized fashion. The at least one primary carrier signaland the at least one secondary signal are digital signals. The scanningprobe instrument also includes a controller communicatively coupled tothe compound sparse sampling pattern generator. The scanning probeinstrument further includes at least one compound sparse sampling signalconverter that receives the digital signals from the controller,converts the digital signals into analog signals; and provides theanalog signals to at least one scan input. The analog signals dictate alevel of sparsity at which an object is scanned by a scanning probeincluding the at least one scan input. At least one object signalresponse converter receives analog scan response signals from at leastobject response detector that detects a response of the object to scansignals directed at the object by the scanning probe instrument. The atleast one object response converter is coupled to the controller andconfigured to convert the analog scan response signals to digital scanresponse signals. A sparse sampling reconstruction system iscommunicatively coupled to the controller. The sparse samplingreconstruction system receives the digital scan response signals fromthe controller, and responsively reconstructs an amalgamate image of theobject scanned by the scanning probe instrument.

Other features and benefits that characterize embodiments of thedisclosure will be apparent upon reading the following detaileddescription and review of the associated drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagrammatic illustration of a sparse sampling scanningsystem in which embodiments of the disclosure may be employed.

FIG. 2 is a graphical representation of one embodiment of a primarycarrier signal path of the disclosure.

FIG. 3 is a graphical representation of a randomized secondary signalpattern (solid line) modulating a primary carrier signal (dashed) towhich it is referenced.

FIG. 4 is a graphical representation of one embodiment of discretesparse sampling coordinates (circular markers) derived from the primarycarrier signal represented in FIG. 2 and the randomized modulatingsecondary signal pattern represented in FIG. 3 .

FIG. 5 is a graphical representation of a smoothed Hilbert stylespace-filling curve path 502, superimposed upon unsmoothed Hilbert stylespace-filling curve path 504.

FIG. 6 is a graphical representation including a scan boundaryencompassing a primary carrier signal path and a region of interest(ROI) containing a primary carrier signal path which is scaled relativeto primary carrier path.

FIG. 7 is a graphical representation consisting of an X-Y sparsesampling embodiment including a scan boundary, serpentine style primarycarrier signal path and a set of randomized sparse sample points definedby the set of plot marker type.

FIG. 8 is a graphical representation of a continuous X-Y parametricequation to generate primary carrier signal path.

FIG. 9 is a diagrammatic illustration of a dual column scanning probeinstrument in which at least some of the embodiments of the disclosuremay be included.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

Embodiments of the disclosure generally relate to sparse samplingapplied to analytical instruments which utilize one or more serialscanning systems, or sub-systems, and computational methods applied toreconstruct amalgamate representations of the object being sparselysensed through interaction with one or more analytical probes andresponse signals collected by one or more response signal detectors.

Acquisition times for serial scanning analytical instruments can bereduced significantly by application of sparse sampling, sub-sampling orcompressed sensing. Such instruments include, by way of example,scanning electron microscopes, electron spectrometers, imaging electronspectrometers, ion microscopes, ion spectrometers, laser confocalmicroscopes and x-ray spectrometers. An object being sensed mayexperience reversible modification (e.g., electron or ion chargeaccumulation) or irreversible modification (e.g., changes in bonding,physical deformation, ion implantation, sputtering) due to interactionwith the analytical probe. Detrimental probe-material interactions arereduced through sparse sampling. Sparse sampling and sparse samplingreconstruction benefits from an approach which mitigates artifacts andlimitations associated with electro-mechanical scanning systems. Sourcesof serial scanning artifacts include, by way of example, dynamichysteresis, slew and non-linear response. Examples of systems subject toone or more artifacts which can influence the quality of sparse samplingand sparse sampling reconstruction include, by way of example, magneticscan devices, electromagnetic scan devices, electrostatic scan devices,electromagnetic probe blanking systems and electrostatic probe blankingsystems.

A sparse sampling approach which mitigates serial scanning artifactswhile allowing higher scanning rates benefits the quality of sparsesampling and sparse sampling reconstruction. Constructing sparsesampling scan patterns which are smooth and predominantly continuous onthe carrier signal scale while simultaneously invoking statisticalrandomness at a discrete modulating perturbing signal scale, mitigatestypical artifacts in electro-mechanical scanning systems and reduces theperformance requirements for, or eliminates the need for, dynamic orhigh-speed probe blanking. An approach which permits a continuouslyvariable and adaptive degree of sparse sampling enables a higher degreeof freedom in the design of scan strategies to probe an object andextract information. Freedom in the degree of sparse sampling and thestructure of the carrier signal pattern enables adaptive scan strategiesbased upon a-priori knowledge of the object being sampled or throughinformation acquired while sensing the object. A-priori knowledge mayinclude geometric information, chemical information and structuralinformation. Information acquired during sparse sampling is derived fromthe probe-object response function over the governing interactionvolume, and in some cases, may permit forward-looking modeling to aidadaptive sparse sampling scan strategies.

In embodiments of the disclosure, a sparse sampling approach employscompound signal convertors. In one embodiment, each element of thecompound signal converter includes a primary carrier signal convertermodulated by a secondary signal converter wherein the output of thesecondary signal converter is referenced to the primary carrier signalconverter output. The secondary modulating signal converter isprogrammatically randomized. One embodiment includes a pair of such“primary-secondary” compound signal converters configured as aprogrammable X-Y scan pattern generator wherein one “primary-secondary”compound signal converter generates the X coordinate and the second“primary-secondary” compound signal converter generates the Ycoordinate, and wherein all outputs are coordinated by a programmablelogic controller. Such a compound signal converter configured as an X-Ypattern generator may be programmed to produce an X-Y pattern includinga plurality of sequential, ordered and randomized X-Y coordinates,wherein each coordinate is the summation of the primary X-Y carriersignal converters and the secondary X-Y modulating signal converters,wherein the latter acts as a randomizing signal added to the former. Inan X-Y scan pattern generator configured in this manner, the X-Y carriersignal pattern can be considered as a “guiding center” path referencedby the programmatically randomized modulating X-Y signal pattern todefine the sparse sampling coordinates. The aforementioned configuredX-Y scan pattern generator is capable of programming a variety ofarbitrarily smooth and arbitrarily continuous X-Y topological curveswhich include a carrier signal X-Y pattern which is programmaticallyrandomized by the modulating signal X-Y pattern and which, in aggregate,generate a randomized sparse sampling X-Y signal pattern.

Through this approach, the degree of sparsity produced by the aggregateX-Y pattern may be smoothly and continuously regulated in increments ofa fractional percent from 0% to greater than 99% sparsity. Statisticalrandomness is imparted through the randomness programmed into theaggregate X-Y modulated signal pattern. Carrier signal X-Y patternssupported through this approach include, by way of example, continuousspace-filling curves, serpentine patterns, fly-back patterns,generalized polygon patterns and custom path coordinates. Compoundsignal converters configured as a pattern generator capable of conveyinga variety of carrier signals which serve as a guiding path perturbed bythe action of a modulating signal creating a randomized pattern ofcoordinates constitutes a versatile and generalized sparse samplingapproach applicable to serial scanning probe instruments. This sparsesampling approaches defined herein mitigate artifacts and/or detrimentalaspects intrinsic to serial scanning probe instruments. Prior toproviding additional details regarding the different embodiments, adescription of an illustrative operating environment is provided below.

FIG. 1 shows an illustrative operating environment in which certainspecific embodiments disclosed herein may be incorporated. The operatingenvironment shown in FIG. 1 is for illustration purposes only.Embodiments of the present disclosure are not limited to any particularoperating environment such as the operating environment shown in FIG. 1. Embodiments of the present disclosure are illustratively practicedwithin any number of different types of operating environments.

It should be noted that like reference numerals are used in differentfigures for same or similar elements. It should also be understood thatthe terminology used herein is for the purpose of describingembodiments, and the terminology is not intended to be limiting. Unlessindicated otherwise, ordinal numbers (e.g., first, second, third, etc.)are used to distinguish or identify different elements or steps in agroup of elements or steps, and do not supply a serial or numericallimitation on the elements or steps of the embodiments thereof. Forexample, “first,” “second,” and “third” elements or steps need notnecessarily appear in that order, and the embodiments thereof need notnecessarily be limited to three elements or steps. It should also beunderstood that, unless indicated otherwise, any labels such as “left,”“right,” “front,” “back,” “top,” “bottom,” “forward,” “reverse,”“clockwise,” “counter clockwise,” “up,” “down,” or other similar termssuch as “upper,” “lower,” “aft,” “fore,” “vertical,” “horizontal,”“proximal,” “distal,” “intermediate” and the like are used forconvenience and are not intended to imply, for example, any particularfixed location, orientation, or direction. Instead, such labels are usedto reflect, for example, relative location, orientation, or directions.It should also be understood that the singular forms of “a,” “an,” and“the” include plural references unless the context clearly dictatesotherwise.

It will be understood that, when an element is referred to as being“connected,” “coupled,” or “attached” to another element, it can bedirectly connected, coupled or attached to the other element, or it canbe indirectly connected, coupled, or attached to the other element whereintervening or intermediate elements may be present. In contrast, if anelement is referred to as being “directly connected,” “directly coupled”or “directly attached” to another element, there are no interveningelements present. Drawings illustrating direct connections, couplings orattachments between elements also include embodiments, in which theelements are indirectly connected, coupled or attached to each other.

FIG. 1 is a diagrammatic illustration of a scanning tool 100 forobtaining a representation of an object 102 in which at least someembodiments of the disclosure may be included. As can be seen in FIG. 1, system 100 includes a scanning probe instrument 104 (e.g., scanningelectron microscope, electron spectrometer, imaging electronspectrometer, scanning ion microscope, imaging ion spectrometer, laserconfocal microscope, x-ray spectrometer, etc.) that includes scan inputs106 for scanning an object such as 102.

System 100 also includes a sparse sampling system 108 that includes atleast one compound signal converter 110 capable of converting both aprimary carrier signal and a secondary modulating signal. Each compoundsignal converter 110 may include a carrier signal converter 112, and asecondary signal converter 114. The secondary signal converter 114 isconfigured to modulate the primary carrier signal converter 112. Anoutput of the secondary modulating signal converter 114 is referenced toan output of the primary carrier signal converter 112. One embodiment ofthe compound signal converter 110 uses a primary signal convertercarrier signal with an output range corresponding to the operable (e.g.,full scale) scan field of the scanning probe instrument scan inputs 106,referenced by a secondary modulating signal converter operating over areduced range and higher rate. One embodiment of compound signalconverter 110 utilizes one digital-to-analog converter (DAC) to convertthe combined signal including the programmable primary carrier signal128 and programmable secondary modulating signal 130, performing thefunction of both carrier signal converter 112 and modulating signalconverter 114.

Another embodiment of compound signal converter 110 uses a DAC as theprimary carrier signal converter 112 and a separate DAC as modulatingsignal converter 114, wherein modulating signal DAC 114 is referenced tothe carrier output of carrier signal DAC 112. The function of the DACsin all embodiments is to convert digital signals conveyed from a sparsesampling pattern generator 119 through a controller 116 into analogsignals (e.g., voltages), which are then conveyed across a suitabletransmission line (e.g., coaxial cable) to the scan inputs 106 of thescanning probe instrument 104. One embodiment of the sparse samplingsystem compound signal converter 110 configures the modulating signalconverter 114 as a DAC which is referenced to a particular bit depth onthe carrier signal converter 112, configured as a DAC. In one embodimentof compound signal converter 110, the modulating signal DAC 114 isreferenced to the bit depth corresponding to a noise floor of theprimary carrier signal DAC 112. In a particular embodiment of compoundsignal converter 110, secondary modulating signal DAC 114 is referencedto the least significant bit of a primary carrier signal DAC 112. Inanother embodiment of compound signal converter 110, using DACs assignal converters, the secondary modulating signal converter DAC 114amplitude is restricted relative to the maximum amplitude of primarycarrier signal converter DAC 112 (e.g., DAC 114 has a smaller voltagerange than DAC 112). In one embodiment of compound signal converter 110using DACs, the secondary modulating signal converter DAC 114 has ahigher frequency response relative to primary carrier signal converterDAC 112 (e.g., DAC 114 is faster than DAC 112). In another embodiment ofcompound signal converter 110 using DACs, the gain of secondarymodulating signal converter DAC 114 referenced to primary carrier signalconverter DAC 112 output is programmable. In one embodiment of thesparse sampling system 108, compound signal converter 110 is configuredas an X-Y pattern generator wherein X includes at least one carriersignal converter 112 and at least one modulating signal converter 114and Y includes at least one primary carrier signal converter 112 and atleast one secondary modulating signal converter 114.

In an embodiment of the sparse sampling system 108 configured as an X-Ysparse sample pattern generator, the carrier signal converter 112 andmodulating signal converter 114 outputs convey through one transmissionline to scanning probe instrument scan inputs 106. In another embodimentof the sparse sampling system 108 configured as an X-Y sparse samplepattern generator, the primary carrier signal converter 112 andsecondary modulating signal converter 114 outputs convey throughseparate transmission lines to scanning probe instrument scan inputs106, the actions of which are both synchronized through controller 116.For example, the primary carrier signals 112 could convey to a set ofupper deflection coils (not shown) of a scanning transmission electronmicroscope and the secondary modulating signals compound signalconverter 114 could convey to a lower set of deflection coils (notshown). The sparse sampling system compound signal converter 110 isextensible to “N” number of signal converter elements. For example,compound signal converter 114 include a primary, secondary and tertiarysignal converter elements. The sparse sampling system 108 is extensibleas a triad of compound signal converters to configure an X-Y-Z patterngenerator. One embodiment of the sparse sampling system 108 configuredas an X-Y-Z pattern generator is suitable for three-dimensional scanningprobe instruments including, but not limited to, a confocal scanninglaser microscope (CSLM).

System 100 further includes one or more object response signalconverters 122 that convert a “response” signal of the object 102 fromone or more object response detector(s) 126. The object responsedetector(s) 126 may be of various types, and depend upon the type(s) ofresponse signals collected from the object 102 (e.g., secondaryelectrons, backscatter electrons, Auger electrons, secondary ions,X-rays.) One embodiment of object response signal converter 122 uses ananalog-to-digital converter (ADC) signal converter or plurality of ADCsto collect signals from the object response detectors 126. Oneembodiment of object response signal converter 122 could include a pulseprocess converter (e.g., to convert x-ray object response detectorsignals). In one embodiment of the sparse sampling system 108, thedegree of oversampling from the object response signal converters 122,relative to the dwell time used to collect the object responsedetector(s) 126 signals induced from the object being sparsely sensed,may be averaged to improve the signal-to-noise ratio (SNR) of theresponse signals. For example, and assuming a sufficiently highbandwidth object response detector 126; a dwell time of one microsecond(1 us) and a sparse sampling system clock rate of 50 MHz (20nanoseconds), would correspond to an oversampling ratio of 50 and allowa corresponding improvement in SNR of over 7. In one embodiment of thesparse sampling system 108, the object response detector(s) 126 operatecontinuously or under the control of the scanning probe instrument 104.In another embodiment of the sparse sampling system 108, the objectresponse detector(s) 126 are operably triggered through the action of aninput-output object response detector(s) 126 element (e.g., a generalpurpose input-output, or GPIO). In an alternative embodiment of thesparse sampling system 108, the object response detector(s) 126 transmita trigger signal to the controller 116 to initiate and/or increment ascan or scan event action.

A controller 116, which may be a part of sparse sampling system 108, isoperably coupled to the primary carrier signal converter 112, thesecondary signal converters 114 and object response signal converter(s)122. Controller 116 coordinates actions among the signal converters 112,114, 122 as well as, in some embodiments, the object responsedetector(s) 126, as noted above. In one embodiment, the controller 116is a programmable logic controller (PLC). In one embodiment, the PLC isconfigured as a field programmable gate array (FPGA). In a particularembodiment, the FPGA functions as a high-speed data transmission array.In one embodiment of the sparse sampling approach disclosed herein, thesparse sampling X-Y pattern coordinates are synchronized by the PLC withresponse signal converter data and accessed through an address listwhich pair the pattern coordinates and the response signals.

In some embodiments, patterns produced by the sparse sampling patterngenerator 119 are adapted to extract information from object 102, basedupon a-priori knowledge 118 of the object 102 being sensed, or to testan expectation of the object 102 being sensed. A-priori object knowledge118 includes, but is not limited to, information of the object 102geometry based upon design information such as from computer aideddesign (CAD) digital content or a graphic design system (GDS) (e.g., aGDSII digital file). A-priori object knowledge 118 could also be derivedfrom lower resolution and/or larger field of view data which providesknowledge of hierarchical congestion and/or geometric density. Examplesof such information include, but are not limited to, optical data orlower resolution data from the same or different scanning probeinstrument. In general, a-priori object knowledge 118 includesstructural information about the object 102, chemical information aboutthe object 102, or any other suitable information.

In a typical operation, the object 102 is placed in proximity to thescanning probe on support 101. In some embodiments, support 101 is afixed platen and the scanning probe is moveable in X-Y or X-Y-Z. In anembodiment with a moveable scanning probe, the scanning probe may movestep-wise or continuously while the object 102 being sensed remainsfixed and stationary. In other embodiments, support 101 is a stage whichis moveable in X-Y or X-Y-Z. In one embodiment wherein the scanningprobe is moveable and the object is placed upon a moveable stage, thesparse sampling approach disclosed herein may be actioned whilesimultaneously moving a stage or sub-stage during the sparse samplingoperations, to allow a continuous or predominantly continuous dynamicsparse sampling pattern to sense the object over an area or volume whichmay extend to construct a continuous, largely continuous, or a pluralityof continuous strips ordered over a one-dimensional, a two-dimensionalor a three-dimensional space. In one embodiment of support 101, thesimultaneously X-Y, or X-Y-Z moving stage is a mechanical piezoelectricstage, a laser interferometric stage, a feedback encoded stage, or anotherwise precision motion stage such that the motion of the objectbeing sensed can be controlled within the aggregate system resolutiontarget. In one embodiment of support 101, the simultaneously movingprecision stage has a step resolution of 1 nanometer or better, alongeach axis.

In one embodiment of support 101, the simultaneously moving precisionstage is a sub-stage affixed permanently or temporarily to an existingprimary stage. In some embodiments, the object and/or the scanning probeis in ambient atmosphere. In other embodiments, the object 102 and/orelements of the scanning probe instrument 104 are in partial vacuum. Thesparse sampling pattern generator 119 produces a sequential set ofpatterns which include a primary carrier signal path and a secondarymodulating signal path, which are conveyed to the controller 116. Whereapplicable, sparse sampling pattern generator 119 will define the dwelltime for each sparse sampling coordinate of the pattern and convey thedwell time data for each coordinate to the controller 116. Typically, adwell time will significantly exceed the scanning probe instrument 104probe transit time between sampling coordinates. In one embodiment ofsparse sampling system 108, the dwell time is programmable for eachdiscrete sparse sampling pattern element. For example, each pixelelement could have a dwell time scaling with the gray scale intensity ofa corresponding image pattern. In one embodiment of sparse samplingsystem 108, the programmable dwell time per sample coordinate may betruncated if a threshold signal-to-noise response signal value isattained, as actioned through the controller 116. For example, if aprogrammable threshold pixel intensity value for a back-scatteredelectron (BSE) object response detector is achieved prior to dwell timeprogrammed for that pixel element; the dwell time will truncate for thatpixel through the action of the controller 116, and in the processreduce overall sampling time.

The controller 116 regulates the sequenced timing and distributes thecoordinated output signals to the compound signal converter 110, whichincludes a primary carrier signal converter 112 and secondary modulatingsignal converter 114. While the scanning probe instrument is functioningunder nominal operating conditions, the sparse sampling system 108conveys output signals from the primary carrier signal converter 112 andsecondary modulating signal converter 114 to the scan inputs 106 (e.g.,external scan inputs, scan amplifiers circuits or deflection coilcircuits of a scanning electron microscope) of the scanning probeinstrument 104. In one embodiment, the sparse sample system 108 is anintegrated component of the analytical instrument and functions as theprimary pattern generator for the scanning probe instrument 104. Inanother embodiment, the sparse sample system 108 interfaces scan inputs106 which are external scan inputs provided by the scanning probeinstrument manufacturer. For example, it is common for external scancontrol inputs to be provided for external scan control on scanningelectron microscopes and scanning transmission electron microscopes, aswell as other scanning probe instruments for use by third-party patterngenerators.

The sequential probe position coordinates are controlled by the sparsesampling system output signals conveyed through the scan inputs 106signal interface to position the scanning probe instrument 104 probe. Ifthe scanning probe instrument 104 probe is a fixed type, the scan inputs106 actions the X-Y or X-Y-Z stage driver interface (not shown) toposition the object scan coordinate proximal to the probe. At eachscanning probe coordinate the probe induces a response from the object102, e.g., secondary electrons in the case of a scanning electronmicroscope or an interactive force in the case of an atomic forcemicroscope, over the duration of the dwell time. The induced objectresponse signal at each scan probe coordinate is concurrently sensed bythe object response detector 126 over the duration of the dwell time.The signal stream induced at each scan coordinate position isconcurrently conveyed through to the object response signal converter122 to the controller 116, which correlates the scan probe positionsignal with the object response signal over the duration of the dwelltime. In one embodiment the object response signal converter 122 signalstream is conveyed in data packets into a memory buffer included incontroller 116. Controller 116 conveys an ordered set of data fromobject response signal converter 122 to an image reconstruction system120, to reconstruct an amalgamate representation of the sparsely sampledobject 102.

In one embodiment of the image reconstruction system 120, the amalgamaterepresentation of the sparsely sampled object 102 being sensed may bereconstructed from the object response signal converter 122 patterncollected through an appropriate object response detector 126, usinginpainting reconstruction methods. A particular embodiment of aninpainting reconstruction method may be beta process factor analysis(BPFA). In one embodiment of the image reconstruction system 120, theamalgamate representation of the sparsely sampled object 102 beingsensed is reconstructed from the object response signal converterpattern collected through an appropriate object response detector usinga down sampling method. One embodiment of the down samplingreconstruction method seeks the pixel element nearest to the missingpixel element and assigns the identical value of the nearest element tothe missing pixel element. Another particular embodiment of downsampling method to reconstruct the amalgamate representation of theobject response signal defines a block of N nearest neighbor pixels(i.e., a block of surrounding pixels where N=8) and, while ignoring theempty pixels in that block, determines the average value of a (??)missing pixel. In another embodiment of the sparse sampling approachdisclosed herein, the amalgamate representation of the sensed object isreconstructed from the sparse sampling pattern using methods based upona Fourier sparse domain.

Examples of how the sparse sampling is carried out are provided below inconnection with FIGS. 2-9 . FIG. 2 is a graphical representation of oneembodiment of a sparse sampling primary carrier signal path produced bysparse sampling pattern generator 119. Representation 200 is scaled forvisualization purposes. Scan boundary 202 encompasses discrete probeposition elements defined by grid pattern 204. A positional grid patternin practice may exceed sixty-four million elements. Scan boundary 202depicts a square rectilinear boundary but scan boundary 202 could alsoencompass a quadrilateral or non-rectilinear boundary. The primarycarrier signal path 206 shown represents a contiguous Hilbert stylespace-filling curve. Circular markers 208 overlaid on the primarycarrier signal path 206 represent discrete primary carrier signal valuesprogrammatically defined along the path 206 which act as referentialvalues for the corresponding secondary modulating signal values. Insparse sampling system 100, the carrier signal patterns may beconstructed from other topological space-filling curves which include,but are not limited to: Hilbert curves, Peano curves, Moore curves,Sierpenski curves, Lissajous curves, and variants thereof.

FIG. 3 is a graphical representation 300 of a primary carrier signalpath 306 identical to path 206 represented in FIG. 2 , now representedas a dotted line, with the additional representation of a randomizedsecondary modulating signal path 308 (solid line). The vertices of eachsolid line segment 308 shown in FIG. 3 represent the X-Y coordinate of adiscrete sparse sampling element within an element of the samplingarray, as defined by the grid 304. It should be noted that the dottedline associated with carrier signal path 306 and the solid line segmentsassociated with modulating signal path 308 are virtual expressions forvisualization purposes. The set of coordinates identified by the markertype 310 define the set of sparse sampling coordinates located withinelements of grid 304. The total number of grid elements defined by grid304 determine the size of the array (e.g., 1024×1024, 2048×2048,4096×4096, 8192×8192) and the corresponding step size expressed in termsof signal amplitude or a resolution spacing.

FIG. 4 is graphical representation 400 of one embodiment of discretesparse sampling coordinates and represented by the circular markers 410with scan boundary 402 and scan grid array 404. The collection of points410 represent the aggregate sum of the primary carrier path 206 in FIG.2 and the randomized secondary modulating signal path 308 in FIG. 3 .Each circular marker 410 in FIG. 4 represents a sparse sampling elementwith programmable dwell time. By choosing a different random seed, or bychoosing a different randomizing algorithm, the same primary carriersignal path (e.g., Hilbert style space-filling path in FIG. 2 ) canproduce a different set of sparse sampling coordinates with the same, ordifferent, degree of sparsity. The degree of sparsity may be regulatedfrom 0% to greater than 99% in fractional percent sparsity incrementsthrough the approach of this disclosure. The distribution of workconveyed to the scanning probe through the action of a primary carriersignal path relative to a secondary modulating pattern may be regulatedby adjusting the scale of the primary carrier pattern, in conjunctionwith the maximum signal amplitude permitted by the secondary modulatingsignal. For example, in one embodiment of sparse sampling system 108,the primary carrier signal has a signal amplitude of ±10V while themaximum amplitude of the secondary modulating signal is ±3 mV. In thisembodiment, the secondary modulating signal may deviate up to ±3 mVrelative to the concurrent position of the primary carrier signal towhich it is referenced. If the maximum permitted secondary modulatingsignal is ±0.5V, then the secondary modulating signal can contribute alarger fraction of the work to construct the same sparse samplingpattern. The signal amplitude voltage corresponds to a physicaldeflection on the scanning probe instrument 104, a motion of the stage,or both. Varying the maximum secondary modulating signal amplitude, asreferenced to the primary carrier signal, and regulating the maximumrate of change of both the primary carrier and secondary modulatingsignals, allows the sampling rate of the sparse sampling scanning probesystem 100 to be varied to mitigate scanning artifacts including, butnot limited to slew, distortion and hysteresis.

A large number of variants are possible in the design of a suitableprimary carrier signal path. FIG. 5 is graphical representation 500, ofa smoothed Hilbert style space-filling curve path 502, superimposed uponunsmoothed Hilbert style space-filling curve path 504. The smoothingoperation on the smoothed Hilbert style space-filling curve path 502represents one variant of a previously described topological curve whichmay be employed in the embodiments of sparse sampling system 108. In oneembodiment of the sparse sampling system 108, the sparse samplingpattern generator 119 may be programmed to construct primary carrierpatterns which are subsequently smoothed or otherwise modified versionsof topological curves and space-filling curves constituting all or partof the primary carrier signals conveyed through to the scanning probeinstrument scan inputs 106 in order to regulate the resulting rate ofchange of the X-Y or X-Y-Z pattern. Regulating the rate-of-change of theprimary carrier pattern is one means to mitigate scanning artifacts suchas, but not limited to slew, distortion and hysteresis.

An embodiment of the sparse sampling system 108 utilizes sparse samplepattern generator 119 to implement a signal pattern which containsregions of interest (ROIs) with varying sparsity and/or scan gridspacing within a scan boundary. FIG. 6 is graphical representation 600including a scan boundary 602 encompassing a primary carrier signal path604 and a ROI 606 containing a primary carrier signal path 608 which isscaled relative to primary carrier path 604. ROI 606 could represent aregion related to geometric boundaries wherein a different samplesparsity was desired and/or a different scan grid spacing was desired(e.g., higher pixel density within ROI 606). A plurality of ROIs mayexist within one scan boundary 602. Graphical representation 600 depictsROI 606 as enclosing a primary carrier signal path 608 constructed usinga non-uniformly scaled version of primary carrier signal path 604, as asimplified visualization. However, primary carrier signal path 608 couldbe constructed from any suitable type of carrier signal path.

FIG. 7 is a graphical representation 700 consisting of X-Y sparsesampling embodiment including scan boundary 702, serpentine styleprimary carrier signal path 704 and a set of randomized sparse samplepoints defined by the set of plot marker type 706. Graphicalrepresentation 700 is useful to illustrate basic features common to thesparse sampling system 108. In this example, primary carrier signal path704 initiates from location 708, transverses along primary carriersignal path 704 and completes at location 710. X-Y coordinate 712represents an arbitrary coordinate along the primary carrier signal path704. The area within circular boundary 716 represents the maximumamplitude of the X-Y secondary modulating signal (not shown), which isreferenced to the primary carrier X-Y coordinate 712 located at thegeometric center of circular boundary 716 along primary carrier signalpath 704. Sparse sample coordinates may be randomly created within anyelement of sample grid 714 located within circular boundary 716. Thecurrent graphical representation 700 consists of a two-dimensional X-Ysparse sampling embodiment and therefore, the sparse sampling system 108allows two degrees of freedom in defining the possible sparse samplelocations within circular area 714. Given a three-dimensional X-Y-Zembodiment of the sparse sampling system 108, the analogousrepresentation of the two-dimensional circular area 714 would be athree-dimensional sphere (not shown). In the case of a three-dimensionalX-Y-Z embodiment of sparse sampling system 108, there are three degreesof freedom in defining the random sparse sampling scan coordinatelocation. The degrees of freedom afforded by the sparse sampling system108 to define sparse sampling coordinates is a significant distinction,as compared to other proposed spare sampling systems.

Further, graphical representation 700 serves to illustrate that anembodiment of sparse sampling system 108 operates given an initial setsparse sample coordinates, such as the set of randomized sparse samplepoints defined by the set of coordinates coincident with marker type706. In an embodiment wherein sparse sampling coordinates are giveninitially, the sparse sampling pattern generator 119 constructs primarycarrier signal path 704 and secondary modulating pattern to fit thea-priori set of sparse sampling coordinates.

An identical set of sparse sample coordinates coincident with the set ofplot marker type 706 in graphical representation 700 may be generated bysparse sampling system 108 using a variety of primary carrier signalpaths. In one embodiment of the sparse sampling system 108, a Hilbertstyle primary carrier signal path is used to generate an identical setsparse sample coordinate coincident with the set of plot marker type 706in graphical representation 700 produced using serpentine primarycarrier signal path 704. Another very simple alternative primary carriersignal carrier embodiment to produce an identical set of sparse samplecoordinates coincident with the set of plot marker type 706 in graphicalrepresentation 700 is represented by a clockwise or counter clockwiseninety-degree rotation of primary carrier signal path 704.

A purpose to invoke a specific primary carrier signal path satisfying agiven set of sparse sampling coordinates includes, but is not limitedto, mitigation of scanning artifacts related to sample charging, whereobject 102 is either insulative or semi-conducting. Both the primarycarrier signal path and the degree of sparsity influence sample chargingin a charged particle scanning probe instrument and may be tuned usingsparse sampling system 108.

One embodiment of sparse sampling system 108 utilizes carrier signalpaths created from a sequential set list of X-Y or X-Y-Z coordinates,including a set of X-Y or X-Y-Z coordinates generated by parametricequations. FIG. 8 is graphical representation 800 of a continuous X-Yparametric equation to generate primary carrier signal path 802.Over-scan boundary 804 encompasses the entire scan area, and object scanboundary 806 (dotted line) represents a sub-region of the primarycarrier signal path 802. It is common practice for pattern generatorsemployed in scanning probe instruments to incorporate an over-scanregion defined by the area between the over-scan boundary 804 and theobject scan boundary 806, the purpose of which is to exclude regionswhere the scan pattern may be non-ideal for reasons including, but notlimited to, non-linear scan behavior and non-uniform area coverage. Theregion within the object scan boundary 806 represents a region of higheruniformity relative to the region between the over-scan boundary 804 andthe object scan boundary 806. The primary carrier signal path 802 inrepresentation 800 initiates at X-Y coordinate 808, follows continuousprimary carrier signal path 802 and terminates at X-Y coordinate 810. Aparticular X-Y parametric equation embodiment to generate space-fillingcarrier signal path 802 is a smoothed form of the parametric equationEquation 1:

$\begin{matrix}{{{X = {A_{x}x{❘{{2\left( \frac{t}{a} \right)} - {{floor}\left( {\frac{t}{a} + \frac{1}{2}} \right)} - 1}❘}}};}{Y = {A_{y}x{❘{{2\left( \frac{t}{b} \right)} - {{floor}\left( {\frac{t}{b} + \frac{1}{2}} \right)} - 1}❘}}}} & {{Equation}1}\end{matrix}$

where, A_(x) and A_(y) define the maximum signal amplitudes for X and Ydimensions respectively. The vertical brackets indicate the absolutevalue of the quantity enclosed. Variable t, is a time incrementparameter, a is the X frequency of the primary carrier signal, b is theY frequency of the primary carrier signal and floor is a mathematicalfunction which takes as input a real number R, and gives as output thegreatest integer less than or equal to R. A large family of X-Y andX-Y-Z parametric equations may be utilized by sparse sampling system 108in order to produce suitable primary carrier signal paths. Lissajouscurves represent yet another particular common family of parametriccurves which can be explored as primary carrier signal paths.

In an embodiment of sparse sampling system 108 employing a continuousspace-filling type path, beam blanking may not be required along thescan path, or along parts of the scan path. Beam blanking is a commonelement in charged particle systems which provides a means toextinguish, or “blank”, the probe interaction with the object.Typically, in charged particle instruments a beam blanking component mayinclude electrostatic deflection plates near the top of the columnproximal to a crossover position in the optical path. Action of the beamblanking deflects the probe (beam) into a position which prevents theprobe (beam) from transmitting through the optical path to interact withthe object. High-speed beam blanking elements are typical optionsavailable in a charged particle embodiment of scanning probe instrument104 which allow more rapid beam blanking, corresponding to higherresolution definition of the dwell time at each scan coordinate. Inanother embodiment of sparse sampling system 108 employing one or morediscrete or continuous primary carrier signal paths, beam blanking maybe utilized as desired to mitigate scan artifacts and spurious probeinteractions with object 102.

A large variety of suitable space-filling carrier signals may beutilized by sparse sampling system 108. Carrier signal patterns may beprogrammed to generate any combination of: a continuous andnon-overlapping pattern; a continuous and non-intersecting pattern; acontinuous and intersecting pattern; or a continuous and overlappingpattern. Sparse sampling system 108 may utilize carrier signal patternsprogrammed as discrete segments with arbitrary discontinuity. Forexample, this approach could be applied to trace and/or fill a pluralityof separate, geometric regions or spatial features of the object beingsensed. A particular example is a carrier signal path and referencedmodulating signal path designed to produce a set of sparse samplingcoordinates which trace the path incorporating a neuron in a biologicalmatrix. Similarly, a rectangular, triangular, circular or othergeometric pattern on the object being sensed could represent thesparsely sampled domain.

Sparse sampling system 108 may utilize carrier signal patternsconstructed from analytical space-filling curves programmaticallymodified to adjust the aggregate sparse sampling pattern, and/or theperformance of the pattern generator, and/or the interaction with thescanning analytical system. For example, the transmitted carrier signalpatterns and referenced secondary modulating signal patterns may besmoothed by software mathematically or by hardware to limit therate-of-change of the signals in order to not exceed the performancelimitations of the scanning probe system in order to avoid scanningartifacts.

FIG. 9 is diagrammatic illustration 900 of a dual column scanning probeinstrument in which at least some of the embodiments of the disclosuremay be included. Scanning electron beam column 902 and focused ion beamcolumn 904 are oriented such that a coincidence region exists betweenthe scan areas of electron beam 946 and ion beam 948. Object 944 surfacearea is depicted as orthogonal to ion beam 948. In one embodiment,object 944 is affixed to a moveable stage (not shown) that allows X-Y-Zas well as rotation and tilt stage motion with range sufficient toorient object 944 surface area orthogonal to electron beam 946 or ionbeam 948. The scanning electron beam column 902 depicted includes anelectron source 906, extraction electrode 908, anode 910,electromagnetic collimating lens system 912, spray aperture 914, in-lensobject response signal detector 916, electromagnetic lens coil body 918,outer pole piece 920, inner pole piece 922, electrostatic objective lenselectrodes 924 and 928, and scanning probe coils 926. The focused ioncolumn 904 includes an ion source 930, extraction electrode 932,condenser lens 934, variable aperture 936, electrostatic deflectionelectrodes 938 and 940, and objective lens 942.

One embodiment of the sparse sampling system 108 of FIG. 1 is configuredwith at least two pair of X-Y compound signal converters 110 tosimultaneously drive the scan coils 926 of scanning electron column 902and scan deflection electrodes 938 and 940 of focused ion column 904.One embodiment of the sparse sampling system 108 includes an objectresponse detector 126 configured as a secondary ion detector and anobject response detector 126 configured as a backscatter electrondetector which operate simultaneously and concurrently with sparsesampling system 108. Additional object response detectors 126 in dualcolumn scanning probe instrument 900 may include, but not be limited to,in-lens secondary electron detectors, in-chamber secondary electrondetectors, in-chamber backscatter detectors, secondary ion conversiondetectors, fluorescence detectors, x-ray detectors, time-of-flightsecondary ion mass spectrometers, electrostatic-electromagnetic massspectrometers, and quadrupole mass spectrometers.

In one embodiment of the sparse sampling system 108, a plurality of X-Ydiscrete layers or thin sections of the object being probed are sparselysampled. The sparse sampling positions from each layer areprogrammatically randomized to produce a sparse sampling volumerandomized in three dimensions, X-Y-Z. For example, sparse samplingsystem 108 drives the scan deflection electrodes 938 and 940 to producean ion milling process by focused ion column 904 to expose a freshobject 944 surface layer (e.g., also could be termed a slice or sectiondefined by the interaction volume of the probe and object). Sparsesampling system 108 drives electron beam column 902 concurrent with, orsubsequent to, the ion milling process to acquire a sparse samplingamalgamate representation of the fresh object 944 surface region usingone or more object response detectors 126 and wherein each sparsesampling X-Y scan has a unique randomized sparse sampling pattern. Theprocess of using sparse sampling system 108 to generate a fresh surfacewith ion beam column 904 and acquire a sparse sampling with electronbeam column 902 is repeated to generate a stack of X-Y amalgamaterepresentations produced by image reconstruction system 120. In thisembodiment, the sparse sampling is extended from two dimensions intothree dimensions and the maximum percentage of sparsity allowed forsuccessful image reconstruction system 120 is much higher than themaximum sparsity allowed for a corresponding two-dimensional individuallayer. For example, if 90% sparsity is the maximum sparsity whichproduces an acceptable amalgamate representation using imagereconstruction system 120 for each individual X-Y scan layer; 97% orgreater sparsity may produce an acceptable amalgamate representationusing image reconstruction system 120 from the same X-Y scan layers whenprocessed as a randomized three-dimensional X-Y-Z stack. Each depthlayer signal pattern includes a programmatically unique randomized X-Ysparse sampling pattern in order to optimize the sparse samplingprocessed by image reconstruction system 120 as X-Y-Z layer stack toyield an amalgamate reconstruction with higher sparsity than can beobtained from each layer individually.

In one embodiment of sparse sampling system 108, the sparse samplingoperation may be repeated successively over the same area using eitheran identical sparse sampling pattern generated from 119 for eachsuccessive scan, or using a uniquely randomized pattern generated from119 for each successive scan pattern, or any combination thereof. Thisembodiment is utilized, for example, to acquire successive X-Y scansduring continuous or semi-continuous sensing of the object 102 beingsparsely sampled.

In one particular embodiment of sparse sampling system 108, the entiresparse sampling process from sparse sampling pattern generator 119through to image reconstruction system 120 operates successively andrepeatedly as rapidly as combined systems permit. Alternatively, theentire sparse sampling system 108 operates with discrete time delay.Highest possible operation rate of sparse sampling system 108, ordiscrete delay operation of sparse sampling system 108, may be used tocontinuously, or semi-continuously, observe the object 102 while it isbeing sparsely sampled. Observations of the object 102 being sparselysampled may include, but not be limited to, changes due to mechanicalmovement of all or part of the object being sensed (e.g., a clockwork orgear motion), modifications induced through the action of a separateprobe (e.g., micromanipulator, laser ablation, focused ion beam, orbroad beam ion milling), changes induced by an energy source (e.g.,heating, cooling), changes due to chemical interaction with all or partof the object being sensed, or any combination thereof. The benefits ofsparse sampling observation of object 102 during such changes includereduced sensing probe interactions with the object 102 being sensed(e.g., reduced electron dose, reduced sample charging), and increasedobject response detector 126 signal acquisition rate during nearreal-time observation.

Successive object response signal detector 126 patterns conveyed throughthe object response signal converter(s) 122 during sparse samplingobservation of object 102 are utilized in one embodiment of sparsesampling system 108 to reconstruct amalgamate representations throughimage reconstruction system 120 to provide a record of change over theobservation period. For example, image reconstructions resulting fromobservations while object 102 is ion milled or mechanically deformedform a three-dimensional volumetric representation from a stack ofreconstructed X-Y amalgamate representations. Alternatively, imagereconstruction system 120 may produce a single X-Y-Z volumetricamalgamate representation from either the entire three-dimensionalsparse data array, or from one or more three-dimensional array sparsedata blocks consisting of subsets of the entire sparse data array. Anexample embodiment is a tomographic reconstruction of a volume basedupon a three-dimensional array of sparse sample data wherein the objectresponse detector 126 is a back-scattered electron detector used toacquire sparse sample object response signal converter 122 data obtainedfrom either sequential focused ion beam milling, or during concurrentfocused ion beam milling, to generate volumetric object 102 responsesignal image data.

In one embodiment of sparse sampling system 108, the sparse samplingpercentage is adapted to reflect changes in the object 102 geometry ormaterial property during observation.

One embodiment of the sparse sampling system 108 utilizes a carriersignal path, a referenced set of modulating signal coordinates and adegree sparsity to suit analytical objectives based upon data from theobject response detector 126 signals induced from object 102 beingsparsely sensed. Analytical objectives may include, but not be limitedto, the response signal intensity (e.g., adjusting dwell time) and/orthe response signal spatial resolution (e.g., adjusting sparsity).

In one embodiment of the sparse sampling system 108, encoding andindexing of the ADC signal data synchronized through the programmablelogic controller may be compressed relative to the full sample signaldata to save significant digital storage memory by storing data in anordered list, rather than as an object array.

In one embodiment of the sparse sampling system 108, object responsesignal converter 122 signals conveyed by the object response detector126 signals induced from the object 102 being sparsely sensed is used tocompute a fast Fourier transform (FFT) from the amalgamaterepresentation from the image reconstruction system 120. In a furtherembodiment of the sparse sampling system 108, the FFT computed from theamalgamate representation is utilized in an automated focus and/or anautomated astigmatism correction method.

One embodiment of sparse sampling system 108 produces X-Y scan patternsdriving the scan deflection electrodes 938 and 940 of focused ion beamcolumn 904 with a sparsity corresponding to an ion dose at or below thestatic Secondary Ion Mass Spectroscopy limit.

In one embodiment of the sparse sampling system 108, sparse samplingpattern generator 119 incorporates scan distortion corrections tocorrect scan distortion errors intrinsic to both the scanning probeinstrument and the sparse sampling system 108. Scan distortion errorsresulting from both the scanning probe instrument and the sparsesampling system 108 are measured using suitable geometric referencestandards. Measured scan distortion error corrections are mapped back tosparse sampling pattern generator 119 to generate signal patterns withminimal scan distortion. Scan distortion errors exhibited by aparticular scanning probe instrument 104 and sparse sampling system 119may be compensated in this manner such that corrected scans are outputby the sampling scan pattern generator 119. A-priori distortioncorrection as described obviates post-process correction ofreconstructed amalgamate representations of object 102.

An embodiment of sparse sampling system 108 includes a point spreadfunction deconvolution (PSFD) operation as part of image reconstructionsystem 120 to combinate sparse sampling reconstruction and PSFD. In thisembodiment the spatial resolution of the amalgamate representation isimproved by inclusion of the PSFD operation and wherein the PSF is ameasured or theoretical function corresponding to scanning probeinstrument 102.

The illustrations of the embodiments described herein are intended toprovide a general understanding of the structure of the variousembodiments. The illustrations are not intended to serve as a completedescription of all of the elements and features of apparatus and systemsthat utilize the structures or methods described herein. Many otherembodiments may be apparent to those of skill in the art upon reviewingthe disclosure. Other embodiments may be utilized and derived from thedisclosure, such that structural and logical substitutions and changesmay be made without departing from the scope of the disclosure.Additionally, the illustrations are merely representational and may notbe drawn to scale. Certain proportions within the illustrations may beexaggerated, while other proportions may be reduced. Accordingly, thedisclosure and the figures are to be regarded as illustrative ratherthan restrictive.

One or more embodiments of the disclosure may be referred to herein,individually and/or collectively, by the term “invention” merely forconvenience and without intending to limit the scope of this applicationto any particular invention or inventive concept. Moreover, althoughspecific embodiments have been illustrated and described herein, itshould be appreciated that any subsequent arrangement designed toachieve the same or similar purpose may be substituted for the specificembodiments shown. This disclosure is intended to cover any and allsubsequent adaptations or variations of various embodiments.Combinations of the above embodiments, and other embodiments notspecifically described herein, will be apparent to those of skill in theart upon reviewing the description.

The Abstract of the Disclosure is provided to comply with 37 C.F.R. §1.72(b) and is submitted with the understanding that it will not be usedto interpret or limit the scope or meaning of the claims. In addition,in the foregoing Detailed Description, various features may be groupedtogether or described in a single embodiment for the purpose ofstreamlining the disclosure. This disclosure is not to be interpreted asreflecting an intention that the claimed embodiments employ morefeatures than are expressly recited in each claim. Rather, as thefollowing claims reflect, inventive subject matter may be directed toless than all of the features of any of the disclosed embodiments.

The above-disclosed subject matter is to be considered illustrative, andnot restrictive, and the appended claims are intended to cover all suchmodifications, enhancements, and other embodiments, which fall withinthe true spirit and scope of the present disclosure. Thus, to themaximum extent allowed by law, the scope of the present disclosure is tobe determined by the broadest permissible interpretation of thefollowing claims and their equivalents, and shall not be restricted orlimited by the foregoing detailed description.

What is claimed is:
 1. A system comprising: a compound sparse sampling pattern generator configured to generate: at least two primary carrier signals defining at least a two dimensional space-filling curve path within a scan boundary; and at least two secondary signals that modulate the at least two primary carrier signals in a randomized fashion in the at least two dimensions of the at least the two dimensional space-filling curve path within the scan boundary; and a controller comprising a non-transitory computer-readable medium, the controller being coupled to the compound sparse sampling pattern generator and configured to receive the at least two primary carrier signals and the at least two secondary signals that modulate the at least two primary carrier signals, wherein the controller further comprises at least one hardware output via which the at least two primary carrier signals and the at least two secondary signals that modulate the at least two primary carrier signals are provided to at least one scan input of a scanning probe.
 2. The system of claim 1 and further comprising: at least two compound sparse sampling signal converters; and the controller communicatively coupled to the at least two compound sparse sampling signal converters, wherein the controller is configured to convey the at least two primary carrier signals and the at least two secondary signals to the at least two compound sparse sampling signal converters.
 3. The system of claim 2 and wherein the at least two primary carrier signals and the at least two secondary signals are digital signals.
 4. The system of claim 3 and wherein the at least two compound sparse sampling signal converters are configured to convert the digital signals into analog signals.
 5. The system of claim 4 and wherein the at least two compound sparse sampling signal converters are communicatively coupled to the at least one scan input that is configured to receive the analog signals, the analog signals dictating a level of sparsity at which an object is scanned by a scanning probe including the at least one scan input.
 6. The system of claim 5 and further comprising the scanning probe including the at least one scan input, and wherein the scanning probe comprises at least one of: scan amplifier circuits; electromagnetic deflection coils; electrostatic deflection coils; piezoelectric deflection systems; optical relays; electromechanical relays; or electromechanical actuators.
 7. The system of claim 5 and further comprising at least one object signal response converter configured to receive analog scan response signals from at least object response detector that detects a response of the object to scan signals directed at the object by the scanning probe, the at least one object response converter coupled to the controller and configured to convert the analog scan response signals to digital scan response signals.
 8. The system of claim 7 and further comprising a sparse sampling reconstruction system communicatively coupled to the controller, the sparse sampling reconstruction system configured to receive the digital scan response signals from the controller, and responsively reconstruct an amalgamate image of the object scanned by the scanning probe instrument.
 9. The system of claim 8 and wherein the sparse sampling reconstruction system is configured to perform at least one of: a Beta-Process Factor Analysis (BPFA) reconstruction; a generalized in-painting reconstruction; a down sampling reconstruction; a Fourier-basis reconstruction; or a nearest neighbor reconstruction.
 10. The system of claim 4 and wherein: the at least two compound sparse sampling signal converters comprise a pair of compound signal converters configured to form an X-Y pattern system; or the at least two compound sparse sampling signal converters comprise a triad of compound signal converters configured to form an X-Y-Z pattern system.
 11. The system of claim 4 and wherein the at least two compound sparse sampling signal converters comprises: at least two primary carrier signal converters; and at least two secondary signal converters; wherein outputs of the at least two secondary signal converters are referenced to outputs of the at least two primary carrier signal converters.
 12. The system of claim 11 and wherein: each of the at least two primary carrier signal converters comprises a first digital-to-analog converter (DAC) configured to convert one of the at least two primary carrier signals into an analog signal; and each of the at least two secondary signal converters comprises a second DAC configured to convert one of the at least two secondary signals into an analog signal.
 13. The system of claim 12 and wherein the second DAC is referenced to a bit depth of the first DAC.
 14. The system of claim 1 and wherein the compound sparse sampling pattern generator is configured to generate the at least two primary carrier signals such that the at least two primary carrier signals provide at least one of a non-overlapping pattern; a non-intersecting pattern; an intersecting pattern; or an overlapping pattern.
 15. The system of claim 1 and wherein the compound sparse sampling pattern generator is configured to generate the at least two primary carrier signals such that the at least two primary carrier signals provide at least one of: two-dimensional space-filling topological curves; or three-dimensional space-filling topological curves.
 16. The system of claim 5 and wherein the compound sparse sampling pattern generator is configured to provide a sub-sampling sparsity that is programmatically controllable in increments of a fractional percent through a range of 0% to greater than 99%.
 17. The system of claim 16 and wherein the sub-sampling sparsity is variable within a scan operation.
 18. The system of claim 11 and wherein the referenced outputs of the at least two secondary signal converters comprise: a sub-sampling pattern; and a sub-sampling pattern programmatically randomized.
 19. A method comprising: generating, by a sparse sampling system having a processor and a non-transitory computer-readable medium, at least two primary carrier signals defining at least a two dimensional space-filling curve path within a scan boundary; and generating, by the sparse sampling system having the processor and the non-transitory computer-readable medium, at least two secondary signals that modulate the at least two primary carrier signals in a randomized fashion in the at least two dimensions of the at least the two dimensional space-filling curve path within the scan boundary.
 20. A scanning probe instrument comprising: a compound sparse sampling pattern generator configured to generate: at least two primary carrier signals defining at least a two dimensional space-filling curve path within a scan boundary; and at least two secondary signals that modulate the at least two primary carrier signals in a randomized fashion in the at least two dimensions of the at least the two dimensional space-filling curve path within the scan boundary; wherein the at least two primary carrier signals and the at least two secondary signal are digital signals; a controller communicatively coupled to the compound sparse sampling pattern generator; at least two compound sparse sampling signal converters configured to: receive the digital signals from the controller; convert the digital signals into analog signals; and provide the analog signals to the at least one scan input, wherein the analog signals dictate a level of sparsity at which an object is scanned by a scanning probe including the at least one scan input; at least one object signal response converter configured to receive analog scan response signals from at least object response detector that detects a response of the object to scan signals directed at the object by the scanning probe instrument, the at least one object response converter coupled to the controller and configured to convert the analog scan response signals to digital scan response signals; and a sparse sampling reconstruction system communicatively coupled to the controller, the sparse sampling reconstruction system configured to receive the digital scan response signals from the controller, and responsively reconstruct an amalgamate image of the object scanned by the scanning probe instrument. 